Question
Write the value of $\big(2+\sqrt3)(2-\sqrt3\big).$
✓
Answer
Given that:
$\big(2+\sqrt3)(2-\sqrt3\big)$
It can be simplified as
$\big(2+\sqrt3)(2-\sqrt3\big)=2\times2-2\times\sqrt3+2\times\sqrt3-\big(\sqrt3\big)^2$
$=4-2\sqrt3+2\sqrt3-3$
$=4-3$
$=1$
Hence the value of the given expression is $1.$
$\big(2+\sqrt3)(2-\sqrt3\big)$
It can be simplified as
$\big(2+\sqrt3)(2-\sqrt3\big)=2\times2-2\times\sqrt3+2\times\sqrt3-\big(\sqrt3\big)^2$
$=4-2\sqrt3+2\sqrt3-3$
$=4-3$
$=1$
Hence the value of the given expression is $1.$
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